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Q1. If  then angle A is a/an _______ angle.

• 1) right
• 2) straight
• 3) obtuse
• 4) acute

Solution

An angle whose measure is greater than 90° and less than 180° is called an obtuse angle.

Q2. In the following figure, angle 1 and 5 are:

• 1) Linear pair of angles
• 2) Vertically opposite angles
• 3) Corresponding angles
• 4) Alternate angles

Solution

Angles 1 and 5 are corresponding angles.

Q3.   Line FB is parallel to Line EC. Use properties of angles to find 'y' :

Solution

We know that, Line FB is parallel to Line EC. Here we can clearly see that,  AOF and CPD are equal alternate exterior angles. Thus, AOF = CPD So, 114 = 2y 2y = 114 (transposing both sides of equation) y = (dividing both sides by 2) i.e., y = 57^o

Q4.

• 1)
• 2)
• 3)
• 4)

Solution

Q5. The reflex angle of 60 is ______ .

• 1) 300^o
• 2) 30^o
• 3) 420^o
• 4) 120^o

Solution

The reflex angle of 60 is 360^o - 60^o = 300^o

Q6. Complementary angle of 55^o is

• 1) 65o
• 2) 25o
• 3) 55o
• 4) 35o

Solution

Complementary angle of 55o is 90o- 55o= 35o.

Q7. In the adjoining figure, the measure of angle a is 50^o, what is the measure of angle b?

• 1) 108^o
• 2) 150^o
• 3) 58^o
• 4) 128^o

Solution

Angle d forms a linear pair with Angle 72^o Thus, d = 180^o - 72^o = 108^o Now, a + b and d are opposite angles so, a + b = d b = d - b b = 108° - 50° b = 58°

Q8. In the figure given below, the measure of y is:

• 1) 130o
• 2) 120o
• 3) 150o
• 4) 30o

Solution

Since, the angle measuring 150o and y are corresponding angles. Therefore, y = 150o. (As the lines are parallel, corresponding angles are equal)

Q9. Which of the following relations is correct for the given figure?

• 1) QR = RS
• 2) QS > PS
• 3) QR < QS > PS
• 4) QR < RS < PS

Solution

The line segment QR is less than the ray RS which is further less than the line PS.

Q10. In the following figure, the measure of angle x is

• 1) 55o
• 2) 35o
• 3) 155o
• 4) 45o

Solution

When two lines intersect each other, the opposite angles formed are equal. Hence, x = 35°

Q11. Find the values of angles y and z in the following figure :

Solution

In the given figure we can see that, AOE = COD [vertically opposite angles] So, COD = z = 43^o Since AOB, BOC, COD are linear pair of angles, thus AOB + BOC + COD = 180^o BOC + COD = 90^o + 43^o = 133^o Thus, AOB = y = 180^o - 133^o = 47^o Thus, y = 47^o and z = 43^o

Q12. Name the different types of angles. Draw an acute angle and obtuse angle of any measure.

Solution

The different types of angles are : (i) Right angle (90^o) (ii) Acute angle (< 90^o) (iii) Obtuse angle (>90^o) (iv) Linear angle (180^o) (v) Reflex angle (> 180^o) (vi) Complete angle (360^o) Acute angles are those angles which measure less than 90^o and obtuse angles have a measure greater than 90^o.

Q13. What is the measure of complement of each of the following angle? (a) 45^o   (b) 54^o   (c) 65^o

Solution

To find the complement of each of the given angle, we have to subtract them from 90^o, since the sum of two complementary angles is 90^o. (a) 45^o Complementary angle of 45^o = 90^o - 45^o = 45^o (b) 54^o Complementary angle of 54^o = 90^o - 54^o = 36^o (c) 65^o Complementary angle of 65^o = 90^o - 65^o = 25^o

Q14. Identify which of the following pairs are complementary and which are supplementary. (a) 68^o, 112^o (b) 55^o, 35^o (c) 79^o, 101^o (d) 64^o, 26^o

Solution

In order to find the complementary pair of angles, add the angles to get 90^o. And to find the supplementary pair, the angle sum should amount to 180^o. (a) 68^o, 112^o Sum = 68^o + 112^o = 180^o Thus, it is a supplementary pair of angles. (b) 55^o, 35^oSum = 55^o + 35^o = 90^o Thus, it is a complementary pair of angles. (c) 79^o, 101^o Sum = 79^o + 101^o = 180^o Thus, it is a sumpplementary pair of angles. (d) 64^o, 26^o Sum = 64^o + 26^o = 90^o Thus, it is a complementary pair of angles.

Q15. In the adjoining figure the measure of angle x is ______ .

• 1) 60^o
• 2) 64^o
• 3) 40^o
• 4) 54^o

Solution

x = = 54°

Q16. Name all pairs of vertically opposite angles in the following figure, where WR and VS are parallel lines and PU and QT are the transversals.

Solution

Given that, WR || VS ; Thus, the pair of vertically opposite angles are : (i) WAP and BAC ; (ii) PAB and CAW ; (III) VCA and UCD ; (IV) ACD and VCU ; (V) QBR and ABD ; (VI) QBA and DBR ; (VII) BDS and CDT ; (VIII) TDS and BDC.

Q17. What are vertically opposite angles? Illustrate.

Solution

When two lines intersect, the angles formed are called vertically opposite angles. Here, the pairs of vertically opposite angles are : 1 and 3 ; 2 and 4

Q18. Name all possible angles formed in the figure given below:

Solution

Name an angle using the vertex and one point on each ray. The vertex is always the middle point. The angles that are formed in the figure are as follows: AOP, POQ, QOR, ROB, AOQ, AOR, POR, POB, QOB and AOB (straight angle 180^o)

Q19. In the figure below, AP is parallel to CD. The size w of angle PAB is equal to 135^o and the size z of angle DCB is equal to 147^o. Find angle ABC.

Solution

Draw BS parallel to AP and CD as shown in the figure below. ABC = ABS + CBS w' and ABS are alternate interior angles So, ABS = w' z' and CBS are alternate interior angles So, CBS = z' Angles w and w' are supplementary which gives w' = 180^o - w = 180^o - 135^o = 45^o Angles z and z' are also supplementary which gives z' = 180^o - z = 180^o - 147^o = 33^oTherefore, we have: ABC = ABS + CBS ABC = w' + z' = 45^o + 33^o = 78^o

Q20. What is the measure of supplement of each of the following angle? (a) 121^o   (b) 77^o   (c) 159^o

Solution

To find the supplement of each of the given angle, we have to subtract them from 180^o, since the sum of two supplementary angles is 180^o. (a) 121^o Supplementary angle of 121^o = 180^o - 121^o = 59^o (b) 77^o Supplementary angle of 77^o = 180^o - 77^o = 103^o (c) 159^o Supplementary angle of 159^o = 180^o - 159^o = 21^o

Q21. In the given figure, if BF||CE, find the value of x.

Solution

Given that BF||CE,  OPE and FOP are co-interior angles and are supplementary.Thus, OPE + FOP = 180^o i.e., 80^o + FOP = 180^o FOP = 100^o Thus, x = 100^o

Q22. In the figure given below, AL||EM. Find the measure of all the interior angles cut by the transversals PK and BN.

Solution

Given:- ACQ = 80^o and LDB = 112^o We have to find:- QCD , ODC , OQC and DOQ QCD + ACQ = 180^o (linear pair of angles) Thus, QCD = 180^o - 80^o = 100^o ODC = LDB (pair of vertically opposite angles) LDB = 112^o Thus, ODC = 112^o ACQ = OQC (pair of alternate interior angles) ACQ = 80^o Thus, OQC = 80^o Now, DOQ + ODC = 180^o (interior angles on the same side of the transversal are supplementary) DOQ + 112^o = 180^o Thus,DOQ = 68^o